Linear Codes for the Sum Mod-2 Multiple-Access Channel with Restricted Access

Transmission of information through a multiple-access modulo-2 adder channel is addressed for the situation that out of a fixed family of N potential users at most some m, m < N are active simultaneously. We assign codes to the N users in a way that the receiver is able to correct any t or less errors and separate the s ≤ m messages without a priori knowledge of the subset of active users. A decoding procedure is presented. The efficiency of our method of code construction is demonstrated by some examples and by an upper bound, that asymptotically tends to zero, on the loss of rate.